*DH and DC are named beneficiaries of a pension.
How does that work, exactly? An amount is paid per month into an account in your FIL’s name?*
Quite.
If the capital was used to buy an annuity, that provides an income for DH and the DCs, where is that income going? Why isn't it going into the family pot to help cover bills?
And I'd take a fair bit of convincing that this is the best thing to do with an inheritance. Annuity rates are poor and the amount will be eroded by inflation.
DSS inherited a fair chunk of money from his GM, which was held in trust with his GF, mother and an uncle acting as trustees. They invested it in property, rental income was also held in trust, and the funds were drawn down for school and uni fees. When he was in his early 20s, he "applied to the trustees" to release the capital so he could buy a house of his own. But none of this money was anything to do with his parents, or GF, they had no claim on it.
I think the OP is perfectly entitled to ask for details about any arrangments made in respect of the inheritance. As a family, they need to do their own financial planning and that includes financial help their DCs might need. And if any of the money is DH's alone, then as his wife, OP has every right to know where they stand.
What isn't all right is for the OP to use any money for the children to avoid going back to work if there isn't enough to go round.
I wonder if money-savvy FIL has tied this all up in a way that protects DH's share in the even of a divorce, or some such?
OP, I'd be asking some very direct questions of your DH, like how much was his inheritance, did it all go on paying off the mortgage, if not, where is it now, how much (if any) is the mortgage on the new house, how is the children's money invested etc. If he doesn't know, or is elusive, you can get a copy of MIL's will from the probate registry (costs about £10).
It sounds to me like you have been sidelined in some important financial decisions, OP.